Summary: 'I
Rigorous error bounds for singu~ar va lues o( a matrix using
the precise scalar product
G. Ale(eld
Summarv. Assume that there are given a real approximation 0
to a simple singular value and real vectors u E Rn and
v E Rm as approximations to the corresponding right and left
singular vectors of areal (m.n) matrix A . Then we consid-
er the problemo( computing rigorous errorbounds for these ap-
proximations. Furthermore we consider an iteration method
which improves these bounds iterative~y.
o. Introduction,
It is weIl known (see [3J.[5J. for example) that i( A is a
real (m.n) matrix with rank(A) = r then there is an or-
thogonal (m.m) matrix' V and an orthogonal (n.n) matrix
u such that
VTAU = r ( 1 )
where (in the case m 2 n )
'.'.
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